Variance and standard deviation · Grade 10
In Grade 10 you learn: standard deviation from a frequency table.
Standard deviation measures how far the data typically are from the mean. A small standard deviation means the values are bunched together. A large one means they are spread out. The variance is the standard deviation squared.
Key facts
- Variance: σ² = (Σ(x − x̄)²)/n = (Σx²)/n − x̄².
- Standard deviation σ = √variance, in the same units as the data.
- From a frequency table: σ² = (Σfx²)/(Σf) − x̄².
- Adding a constant to every value moves the mean but does not change σ.
- Multiplying every value by k multiplies the mean and σ by k (and the variance by k²).
- Some courses also use the sample standard deviation, dividing by n − 1. Check which one a question asks for.